00:03As-salamu alaykum dear viewers, dear viewers,
00:07जैसा के previous lecture में हमने types of vectors के बारे में study करी थी,
00:14previous lecture में हमने 12 types of vectors पढ़े थे,
00:19आज भी हम types of vectors के बारे में study करेंगे,
00:23मतलब के जो remaining type है, unit vectors, unit vector के बारे में आज हम study करेंगे,
00:41Now, unit vectors, unit vectors क्या होता है, unit vectors का काम क्या होता है,
00:52unit vector को हम कैसे define करेंगे, के vectors having magnitude unity are 1,
00:59means ऐसा vector जिसका magnitude क्या हो, 1 हो, means unity हो,
01:05तो उसे हम unit vector कहेंगे, unit vector का काम क्या होता है,
01:10it is only used to determine the direction of a vector, means physical quantity,
01:17अच्छा, यह unit vector हम क्यों इस्तिमाल करते हैं,
01:21किसी भी vector का, means किसी भी physical quantity का direction,
01:27determine करने के लिए, हम unit vector का इस्तिमाल करते हैं,
01:32अच्छा, unit vector को कैसे हम define करेंगे,
01:37a vector
01:43having magnitude
01:52unity
01:54or 1
01:58is known as
02:05unit vector
02:09means, ऐसा vector, जिसका magnitude, unity, या जिसे हम 1 हो,
02:16तो उस vector को हम क्या कहेंगे, unit vector कहेंगे,
02:20unit vector का काम क्या होता है,
02:23it is
02:27used
02:27to determine
02:33the direction
02:39of
02:41a physical point T
02:50means
02:52means, vector,
02:56unit vector का का काम होता है,
02:59to determine the direction of a physical quantity or vector,
03:02means, किसी भी physical quantity,
03:05means, vector, vector का direction, determine करने के लिए, हम unit vector का इस्तिमाल करते हैं,
03:11इसका मतलब है,
03:12means, कोई भी vector हो वो, जिस्ट हमें magnitude के फार्म में अप्टेंट हो,
03:17तो उसको vector फार्म में लाने के लिए हम क्या करते हैं,
03:21मिर्पे साथ, मिर्प में magnitude के साथ, unit vector multiply करवाते ही,
03:26then
03:26we know that
03:39vector
03:40vector
03:41vector is equal to
03:47magnitude
03:48into unit vector
03:56vector
03:57magnitude
03:58into unit vector
04:00vector is equal to magnitude
04:02into unit vector
04:03unit vector
04:05किसे हम मालूम करेंगे
04:07so is vector
04:09suppose vector
04:11is equal to
04:13magnitude
04:14magnitude को हम ऐसे भी लिख सकते है
04:17into unit vector
04:19unit vector
04:21को हम
04:22cape देते है
04:24so vector is equal to magnitude
04:27into unit vector
04:28या इसको हम ऐसे भी लिख सकते है
04:30magnitude
04:30into unit vector
04:34तो unit vector
04:36अगर हम find करना चाहें
04:37तो कैसे find करेंगे
04:38so unit vectors
04:43will be equal to
04:44यहां पर magnitude
04:46multiply कर आए तो बराबर भी इस साइड डिवाइड करेगा
04:48so it will be vectors
04:52divided by
04:54magnitude of vector
04:59means unit vector किसके एक्योल हो का
05:02vector divided by
05:03its magnitude
05:04किसका magnitude
05:06is vector का magnitude
05:08so unit vectors
05:09will be equal to
05:13vectors
05:16divided by
05:17its magnitudes
05:18इसको हम ऐसे भी लिख सकते है
05:21vector divided by
05:21its magnitude
05:25unit vector को हम ऐसे अप्तें करते है
05:28means it is obtained
05:35unit vector
05:37it is obtained
05:47by dividing
05:54vector
05:58with its
06:07magnitudes
06:09means unit vector को हम कैसे अप्तेंड करते है
06:11जब vector को उसके magnitude के साथ
06:15divide करवाते है
06:16तो उस condition में हमें unit vector
06:18obtained होता है
06:19अच्छा
06:20Cartesian coordinate system में unit vector
06:24in Cartesian coordinate system
06:32means x-axis, y-axis and z-axis
06:36x-axis पे कों सा unit vector उसका है
06:39along x-axis the unit vector is i
06:42along y-axis the unit vector is j
06:45along z-axis the unit vector is k
06:49means unit vector along x-axis
06:52x-axis की जगे पर जो unit vector use होता है
06:55wo i होता ही
06:56और y-axis की जगे पर जो unit vector use होता है
07:00वो j होता है
07:01means small j
07:02और z-axis की जगे पर जो unit vector
07:05क्योचिश इस्तिमाल होता है
07:06which is small key
07:08Now we have an example of the unit vectors which is the magnitude of 1.
07:22For example, if a vector is equal to 3,
07:373i plus 2j then its unit vectors will be what means we have to calculate its unit vector
07:51and also magnitude of unit vectors means unit vector bhi ista find kareenge uske baad magnitude
08:02of unit vector bhi find kareenge. So as we know that first unit vector calculate kareenge
08:11unit vector kiske equal ho ta hai vector divided by its magnitude. So as unit vectors is equal
08:19to vector divided by its magnitude. So vectors we have obtained 3i plus 2j. Magnitude
08:34kaise calculate kareenge? Under root me x square plus y square plus z square.
08:42Here we have two axes obtained x and y. Means unit vectors x ki jage per i means
08:49jahaan per i ho unit vector to we have to understand x ka value. And this number
08:55means unit vector kareenge we have to understand y axis. So we have to understand y axis
09:02y axis per value. Here we have to understand z axis ka value absent. Means naihi hai.
09:06Toh abhum unit vector kareenge unit vector kareenge unit vector will be obtained is vector means
09:16vector a is the value of vector is 3i plus 2j divided by its magnitude. Acha magnitude
09:24abhum kaise maalum kareenge? Dekhi the value of x is 3 and the value of y is 2. So the
09:32square
09:33on x so the square on x so the square on 3 plus square on y so the square on
09:392. So unit vector
09:44will be obtained is 3i plus 2j upon the square of 3 is 9 the square of 2 is 4.
09:56So unit vector
09:57will be obtained is 3i plus 2j divided by 9 plus 4 it will be 13 means under root 13.
10:10So
10:13this is the value of unit vector is obtained is 3 upon under root 13i plus 2 upon under root
10:2913j. So this is the value of unit vector.
10:39Now we will find its magnitude. Now we will find its magnitude.
10:58So if you have in this value of unit vector we will find its magnitude. So unit vector is 3
11:17upon under root 13
11:21whole square plus y ka square so this is the value of y
11:26क्योंकि यहां पर unit vector j है तो j कोन सी x पर होता है y पर
11:31so this is the value of y so 2 upon under root 13 whole square
11:41so the square of 3 is 9 and the square of under root 13 is 13 square or under root
11:54opposite me cancel हो जाएंगे तो यहां पर 13 बचेगा फिलस the square
12:00of 2 is 4 the square of under root 13 is also 13 तो इसको हम कैसे find
12:08करेंगे यहां पर हम क्या करेंगे प्लस है तो LCM लेंगे
12:13so the magnitude of unit vector will be the LCM of 13 is 13 so 13 का 13 पर
12:23one time table so it will be 9 into 1 9 प्लस यहां पर 13 है तो 13 का
12:2913 पर table one time लगेगा so 4 into 1 it will be 4 so 9 प्लस 4
12:38under root 13 upon 13 so the table of 13 on 13 is one time so it will be under
12:46root
12:461 the under root of 1 is 1 देखे इस unit vector का जो हमें magnitude मिला
12:57which is one means हम कह सकते हैं के this is a unit vector means ऐसा
13:03vector जिसका magnitude one हो तो उसे हम क्या कहेंगे that vector is known as
13:10unit vector तो आज हमने unit vector के बारे में पढ़ा और उसका magnitude
13:17we find करा के कैसे उसका magnitude one होता है so dear students
13:22that was about today's lecture thank you Allah आफेज
